Conic Sections

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Conic Sections

• The EllipsePart A

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Ellipse

• Another conicsection formedby a plane
  intersecting acone
• Ellipse formed when

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Definition of Ellipse

• Set of all points in the plane
• Sum of distances from two fixed points(foci) is
  a positive constant

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Definition of Ellipse

• Definition demonstrated by using two tacks and a
  length of string to draw an ellipse

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Graph of an Ellipse
Note various parts of an ellipse
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Deriving the Formula

• Note
• Why?
• Write withdist. formula
• Simplify

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Major Axis on y-Axis

• Standard form of equation becomes
• In both cases
• Length of major axis 2a
• Length of minor axis 2b

Link to Animated Web Page
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Using the Equation

• Given an ellipse with equation
• Determine foci
• Determine values for a, b, and c
• Sketch the graph

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Find the Equation

• Given that an ellipse
• Has its center at (0,0)
• Has a minor axis of length 6
• Has foci at (0,4) and (0,-4)
• What is the equation?

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Ellipses with Center at (h,k)

• When major axis parallelto x-axis equation can
  be shown to be

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Ellipses with Center at (h,k)

• When major axis parallelto y-axis equation can
  be shown to be

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Find Vertices, Foci

• Given the following equations, find the vertices
  and foci of these ellipses centered at (h, k)

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Find the Equation

• Consider an ellipse with
• Center at (0,3)
• Minor axis of length 4
• Focci at (0,0) and (0,6)
• What is the equation?

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Assignment

• Ellipses A
• 1 43 Odd